Altitude of Satellites above the Surface of the Earth

A) Suppose you are on Earth's equator and observe a satellite passing directly overhead and moving from west to east in the sky. Exactly 12.0 hours later, you again observe this satellite to be directly overhead. How far above the earth's surface is the satellite's orbit?

B) You observe another satellite directly overhead and traveling east to west. This satellite is again overhead in 12.0 hours. How far is this satellite's orbit above the surface of the earth?

2. Relevant equations
T=(2πr^3/2)/(√Gm)

3. The attempt at a solution
Well, I thought that they would both have the same altitude since they have the same period. This is evidently not correct since the back of the book has two different answers for A and B.

I plugged in the numbers for the variables. I dropped the units. I would have looked very messy.

86400=(2πr^3/2)/(√(6.67x10^-11)(5.97x10^24))

I solved for r

r=42226910.15m

altitude= r-Re=35846910.18m which matched what the book has as an answer for B, but why is this the answer for B. Why would they both have different altitude if they have the same period, but in opposite direction? May I get any hint for part A and some clarification on part B?

Well, from the description in the problem, I thought that they were both geosynchronous satellites. If so, would not that make them have the same period? The only difference would be that one is going in the direction of the earth's rotation and the other is going in the opposite direction.

A geosynchronous orbit is an orbit in which the satellite is locked over one place relative to the earth. The earth and the satellite would have the same orbital velocity. On a second thought, I don't see a lot of evidence to support the geosynchronous orbit hypothesis. They may have fast orbital velocity that would allow them to appear again on the same spot after a given time interval.

Staff: Mentor

The satellites appear directly above the observer at the initial time and 12 hours later, but not in between. That rules out geostationary satellites (it would also make "move east to west" and "west to east" wrong).

How does the position of the observer on earth (relative to a non-rotating frame) change during 12 hours?

The satellites appear directly above the observer at the initial time and 12 hours later, but not in between. That rules out geostationary satellites (it would also make "move east to west" and "west to east" wrong).

How does the position of the observer on earth (relative to a non-rotating frame) change during 12 hours?

So, after completing half a period on earth, the satellite appears again. Does that mean that the satellite completed 1.5 times the period of the earth?

What does "1.5 times the period of the earth" mean? The number 1.5 is correct for one of the satellites, I'm not sure if the interpretation is correct as well.

Sorry for not being very clear. I meant that the satellite must have circled the earth 1.5 times for it to satisfy the information of when it was observed the second time. When it was spotted the first time in situation A, it was not seen in the sky until 12 hours later. This means that the satellite passed the point at witch it was spotted the first time. It was heading toward the east then it came back to the original spot in the sky when it was first observed, but the observer was already gone due to the rotation of the earth. Then, when it continued going around the earth, it reached the point where the observer is at. This happened twelve hours later of when it was originally observed.